Evaluate: (1)/(4) \times (z+3z)+7=-z+1

Expression: $\frac{ 1 }{ 4 } \times \left( z+3z \right)+7=-z+1$

Collect like terms

$\frac{ 1 }{ 4 } \times 4z+7=-z+1$

Cancel out the greatest common factor $4$

$z+7=-z+1$

Move the variable to the left-hand side and change its sign

$z+7+z=1$

Move the constant to the right-hand side and change its sign

$z+z=1-7$

Collect like terms

$2z=1-7$

Calculate the difference

$2z=-6$

Divide both sides of the equation by $2$

$z=-3$